A hierarchical stochastic queuing model is presented that consists of a set of processing elements (PEs) and a single queue/server pair representing the shared memory. The model takes into account not only global system behavior but also behavior of tasks on each processing element and probabilistic task migration among the PEs. It is shown that through the use of repeated aggregation each PE can be treated as a queue/state-dependent server pair. This reduction results in an immense simplification of the model. A CPU sensitivity analysis of this reduced model shows that at high CPU service rates, varying the CPU speed has a negligible effect on the server's state-dependent service rate, whereas at low CPU service rates, varying the CPU speed has an effect that depends on the local branching probabilities. Global performance metrics are then obtained on the basis of this reduction